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Review Components

Review Components. Do Now: Draw a vector that is 40 m/s at 40° North of West What is the x component of the velocity and the y component of the velocity? Solve both graphically (with an appropriate scale) and by using trig. Quick Experiment.

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Review Components

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  1. Review Components Do Now: Draw a vector that is 40 m/s at 40° North of West • What is the x component of the velocity and the y component of the velocity? • Solve both graphically (with an appropriate scale) and by using trig

  2. Quick Experiment • If two forces act on an object, how can the forces be arranged to get the maximum force? The minimum force? A force in between the maximum and the minimum? • Work with your partner. Choose an object on your desk. Each partner applies a force with your force producer (finger). Figure answer.

  3. Resultant • A single vector that represents the same affect as the addition of 2 or more vectors • Represented as a dashed line

  4. Two Vectors in the Same Direction Mathematically • 0° angle between them • Add the magnitudes of the vectors together • The resultant is the maximum value possible

  5. Aim: How can we add two vectors together acting on a point? A girl walks 200 m East and then walks another 400 m East. Draw a scaled representation. Scale: 1 cm = 100 m Resultant = 600 m

  6. Two Vectors in Opposite Directions Mathematically • 180° angle between the vectors • Subtract the magnitude of the two vectors • The direction of the resultant is the same as the direction of the larger vector • The resultant is the minimum value possible

  7. A boy runs 50 m West and then runs 20 m East. What distance did the boy run? 70 m What is the boy’s resultant displacement? Scale: 1 cm = 10 m Resultant = 30 m

  8. Range of Possible Values • When two vectors are added together, the resultant can be between the maximum value (when the angle is 0°) and the minimum value (when the angle is 180°) • Example: Is 9 N a possible value when the forces of 30 N and 20 N act concurrently on an object? • No: the range of values is 50 N maximum and 10 N minimum. 9 N falls outside of that range.

  9. A 5 N force directed North and a 3 N force directed East act concurrently (acts on the same point at the same time) Draw the two vectors (Hint: start with a set of axes) Scale: 1 cm = 1 N N E W S

  10. Make a parallelogram • The resultant is constructed from the origin of the two vectors to the opposite corner • Measure the magnitude with the ruler and the angle with the protractor 5.7 cm = 5.7 N 59° North of East N W S

  11. Adding Two Vectors at Right Angles Mathematically • Magnitude is obtained through the Pythagorean Theorem a2 + b2 = R2 (3 N)2 + (5 N)2 = R2 9 N2+ 25 N2 = R2 34 N2 = R2 R = 5.8 N N 5 N W 3 N S

  12. The angle is obtained through SOHCAHTOA N 5 N θ W 3 N North of East S

  13. Solve the following problems mathematically and graphically using an appropriate scale A moterboat can move with a velocity of 4 m/s. What is the resultant velocity if: • The boat is traveling with a current of 2.5 m/s south? • The boat is traveling against a current of 2.5 m/s south? • The boat is trying to move perpendicularly (west) across a stream that is flowing south with a current of 2.5 m/s?

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